Crystal-field coefficient

The angular and distance information provided by the lanthanide induced shift has found widespread application from the determination of solution structures of Ln chelates [18,19] to gaining structural information on proteins, nucleotides and amino acids [19], More recently anion binding to coordinatively unsaturated lanthanide complexes has been effectively signalled as the observed lanthanide induced shift has been directly correlated to the nature of the donor atom in the axial position [8,20,21], It is the polarisability of the axial donor that ranks the second order crystal field coefficient, B02, and hence determines the magnitude of the observed shift. Values of the mean shift of the four most-shifted axial protons of the 12-Nq ring for [Yb.la]3+ are collated in Table 2. 

D crystal-field coefficient (Wang and Kleematm 1991) demagnetization anisotropy... 

Very often, the varions Ln + complexes of a particular ligand are isostructural and the crystal field coefficients are invariant along the Ln + series. Then, F and D can be determined by hnear regression if the A values of a ligand nucleus are known for two or more Ln + cations. To test the assumption that the complex structures and the crystal field coefficients do not vary along the Ln + series, it is convenient to rewrite equation (11) in two linear forms ... 

Discrimination between these two situations is possible for complexes with (effective) axially symmetric magnetic susceptibiUties (G2 = 0). Then it is possible to factor out the remaining crystal field coefficient. Several procedines to achieve this have been outlined in the literature For example, equation (14) can be derived, where A, and Akj denote the paramagnetic-induced shifts (after subtraction of the diamagnetic contributions) of two given ligand nuclei, i and k, by Ln + ion, j, where Rit = GijGt. 

Judd (1962) and independently Ofelt (1962) worked out the theoretical background for the calculation of the induced electric dipole matrix element. The basic idea of Judd and Ofelt is that the intensity of the forbidden f- f electric dipole transitions can arise from the admixture into the 4f configuration of configurations of opposite parity (e.g., 4f d and 4f " n g ). As already mentioned in the introduction, we will unravel here in detail the theoretical model developed by Judd. Special attention will be given to the dimensions, units and selection rules. Our symbolism is close to Judd s. The difference is that we represent the crystal-field coefficient by (instead of Judd s Atp), the light polarization by p (instead of Judd s q), and the additional quantum number by r (Judd s y). 

Note that the dimension of the crystal-field coefficient Akq is energy whereas the dimension of the crystal-field parameter 5 is ML T", or energy (Gorller-Walrand and Binnemans 1996). The 5 include the radial integral r. The Hamiltonian for the crystal-field perturbation is written here as a potential, because this is commonly done in the literature. 

If it is assumed that the crystal field coefficients are constant and that the series of lanthanide complexes are isostructural, then a plot of (LIS),y/(S2) versus Cjl Sf)j or... 

---